Final answer:
The coordinates (8, 8), (6, 6), (8, 4), (10, 6) form a geometric figure with equal side lengths and right angles, identifying it as a square.
Step-by-step explanation:
The set of coordinates given represents a geometric figure that can be identified by plotting the points and examining the shape they form. Plotting the points (8, 8), (6, 6), (8, 4), and (10, 6) on the coordinate system and connecting them in order, we get a closed figure.
By analyzing the distances between the vertices, we can determine that each side of the figure is of equal length, which suggests that it could be a rhombus or a square. Since a square is a specific type of rhombus where all angles are right angles, we need to check the angles formed by the connecting lines. If we find that the angles between each pair of adjacent sides are 90 degrees, then the coordinates form a square.
After evaluating the slopes of the lines connecting the points, we see that they are perpendicular to each other. Therefore, the figure has equal side lengths and right angles, which confirms that the coordinates (8, 8), (6, 6), (8, 4), (10, 6) represent a square.